VIBRANT ACADEMY PHYSICS

CLASS TEST - 1
(India) Private Limited
IRP Class test-1
JEE ADVANCE
IRP ADVANCE TIME : 75 MIN.

MECHANICS-1
Single Choice Question :
1(i). The horizontal component of impulse provided by string tension in moving from extreme point to lower most
point

(A) m 2gh


(B) m 2gh (1 – cos )

h v=0
(C) m 2gh cos 

(D) can’t be found without knowing tension as a function of time

2(ii). In the above question, if mass takes time t in reaching lowermost position, the magnitude of impulse of
tension in string :

(A) mgt + m 2gh

(B) mgt – m 2gh

(C) (mgt )2  2m 2 gh

(D) can’t be found without knowing tension as a function of time

Comprehension (Q.3 to Q.5)

A small bead B of mass m is free to slide on a fixed smooth vertical wire, as indicated in the diagram. One
end of a light elastic string, of unstretched length a and force constant 2mg/a is attached to B. The string
passes through a smooth fixed ring R and the other end of the string is attached to the fixed point A, AR being
horizontal. The point O on the wire is at same horizontal level as R, and AR = RO = a.

rod
fixed
a ring R A
O


bead B

3. In the equilibrium position, find OB

(A) a (B) a/4 (C) 2a (D) a/2
4. The bead B is raised to a point C of the wire above O, where OC = a, and is released from rest. Find the
speed of the bead as it passes O

(A) 2 ag (B) ag (C) ag / 2 (D) ag / 3

5. Find the greatest depth below O of the bead in the subsequent motion
(A) a (B) a/4 (C) 2a (D) a/2

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One or more than one correct :
6. A small steel ball B is at rest on the edge of a table of height 1 m. Another steel ball A, used as the bob of
1 metre long simple pendulum, is released from rest with the thread at horizontal position. Ball A collides with
ball B as shown in the figure. Ball A stops after collision with B and ball B is projected horizontally with
velocity which ball A had just before collision. Consider the motion of B only in air till it hits the ground.

1m
A

1m

(A) ball A is in motion for longer time (B) ball B is in motion for longer time
(C) ball A has greater path length (D) ball B has greater path length

Match the Column :

7. Consider a one-dimensional collision that involves a body of mass m1 originally moving in the positive x
direction with speed v 0 colliding with a second body of mass m2 originally at rest. The collision could be
completely inelastic, with the two bodies sticking together, completely elastic, or some where in between.
After the collision, m1 moves with velocity v 1 while m2 moves with velocity v 2. Match the velocities in
column-I with possible values in column-II.
Column I Column II
(A) If m1 > m2, then v 1 (P) –0.5 v0
(B) If m1 > m2, then v 2 (Q) 0.2 v0
(C) If m1 < m2, then v 1 (R) 0.9 v0
(D) If m1 < m2, then v 2 (S) 1.5 v0
(T) 1.9 v0

8. There is a square frame ABCD of 4 rods of mass m and length L each. The frame is placed in x-y plane as
shown. AC is a line in x-y plane that is taken as w-axis. z-axis is perpendicular to xy-plane through M. M is
mid point of AD. Ix, Iy, Iz, Iw are moments of inertia about x, y, z, w axes respectively.

Column-I Column-II
5ML2
(A) Ix (P)
3 y
is
2 -ax
10ML w
(B) Iy (Q) D C
3
x
7ML2 M
(C) Iz (R)
3 A B

2ML2
(D) Iw (S)
3
(T) None of these

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Subjective :
9. One end of a spring is attached to a wall, and the other is attached to a block which can slide along a rough
horizontal surface. The block kept on a rough surface is pushed towards left from natural length (at point O)
of spring up to point A, where OA = 24 cm. Work done by spring from O to A is W S. Now block is released.
When the spring comes to it’s natural length kinetic energy of block is half of |W S|. How far (in cm) can the
object move from the point A ?

A O
10. A homogeneous flexible chain rests on a wedge whose side edges make angles  = 53° and
 = 37° with the horizontal (refer figure). The central part of the chain lies on the upper rib C of the wedge.
The wedge is pulled to the left along the horizontal pl ane in order to prevent the displacement of the
g
chain with respect to the wedge? If acceleration of wedge is m/s2 then what is value of n. [g is acceleration
n
due to gravity. Consider all surfaces to be smooth]

11. A particle is suspended by a light vertical inelastic string of length ‘’ from a fixed support. At its equilibrium
position, it is projected horizontally with a speed 6g . What is the ratio of the tension in the string in its
horizontal position to that in string when the particle is vertically above the point of support ?
12. In figure shown, the masses of all the blocks are same. The pulleys are frictionless and massless. System
is released from rest. Find displacement (in m) of the shaded pulley in 9 second.

13(i). A beam with mass 4 kg and length 2 m can pivot freely about a hinge at its lower end as shown in figure. A
horizontal force F = 8 N is applied at the top of the beam and the beam is kept vertical by a cable that makes
an angle 37º with the ground and attached to the centre of the beam. (Take sin 37º = 0.6). If the tension in the
string is T Newton, find the value of T/10.
F
M = 4 kg L=2m
37º

14(ii). IN THE ABOVE QUESTION, find the horizontal component (in N) of the force of the hinge on the beam.
15. Find maximum compression (in cm) of spring if collision is elastic in the figure shown. Given m = 2 kg,
3
V0  m/s,Spring constant K = 400 N/m.
4
V0

2m K
m m
=0

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 CLASS
VIBRANT TEST
ACADEMY
(India) Private Limited
- IRP
2PHYSICS
Class test-2
JEE ADVANCE
IRP ADVANCE TIME : 75 MIN.
MECHANICS-2
One or more than one correct :

1. The P.E. of a particle oscillating on x-axis is given as U = 20 + (x – 2)2, here U is in Joules and x is in meters.
Total mechanical energy of particle is 36 J. Choose the correct option(s)

(A) The mean position is at x = –2 m (B) Maximum K.E. of the particle is 16 J

(C) Force on the particle is zero at x = 2 m (D) Minimum potential energy of the particle is 16 J

2. The system shown in figure is released. Forces are horizontal and all surfaces are also horizontal.  is the
symbol for friction coefficient. Choose the correct option(s).

(A) Acceleration of 3 kg block is 2 m/s2

5 Nt 2 kg  = 0.2
(B) Force of friction between the blocks is 1 N. 3 kg
10 Nt  = 0.1
(C) Acceleraton of 2 kg block is 0.5 m/s2

(D) Force of friction between the blocks is 4 N

3. Three spheres each of mass m can slide freely on a frictionless horizontal surface. Sphere A and B are
attached to an inextensible, inelastic massless cord of length L and are at rest in the position shown, when

sphere B is struck directly (head-on collision) by sphere C which is moving to the right with velocity V  V0 î .

Assuming that cord is slack when sphere B is struck by sphere C & assuming perfectly elastic impact,
choose the correct option(s).

3 V0 V0
(A) when the cord gets taut, speed of sphere A is C B B
4 y

7 V0 x L/2 L
(B) when the cord gets taut, speed of sphere B is
4 z
A
7 V0
(C) when the cord gets taut, speed of sphere B is
2
(D) Kinetic energy is not conserved, when the cord gets taut

4. Two balloons are simultaneously released from two building A and B. Balloon from A rises with constant
velocity 10 ms–1. While the other one rises with constant velocity of 20 m s–1. Due to wind the balloons
gather horizontal velocity v x = 0.5 y, where ‘y’ is the height from the point of release. The buildings are at
distance of 250 m & after some tine ‘t’ the balloons collide. Choose the correct option(s).
(A) t = 5 sec.
(B) difference in height of buildings is 100 m
A
(C) difference in height of buildings is 500 m
B
(D) t = 10 sec.
x
250 m

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 x max
5. A particle on a spring executes simple harmonic motion. When the particle is found at x = the
2
(A) speed = v max/2 (B) speed = 3 v max / 2
(C) acceleration = 3 a max / 2 (D) acceleration = amax/2

Subjective :
6. A uniform square plate of mass m = 100 gm and side a = 24 cm can rotate about a smooth vertical axis
passing through one edge. It is initially at rest. A particle of mass m = 100 gm is moving horizontally and
perpendicular to the plane of the plate with velocity u = 70 cm/s. It collides with the plate at the centre of the
plate and after collision its velocity is 10 cm/s in opposite direction. Find the angular velocity (in rad/s) of the
plate just after collision?

7. A particle is initially at rest at the top of a curved frictionless track. The x and y-coordinates of the track are
x2
related in dimensionless units by y  , where the positive y-axis is in the vertical downward direction and
4
positive x-axis is towards right. As the particle slides down the track, its tangential acceleration is a
(in m/s2) at x = 3m is a. O x
13 a Track
Then the value of is
10
y
8. A solid homogeneous cylinder of height 'h' and base radius 'r' is kept vertically on conveyer belt moving
horizontally with an increasing velocity v = a + bt2. If the cylinder in not allowed to slip then time t is taken
6 rg
when the cylinder is about to topple. t = then the value of x is :
xbh

9. The slopes of the windscreen of two motorcars are 1 = 30º and 2 = 15º respectively. At what ratio v 1/v 2 of
the velocities of the cars will their drivers see the hailstones bounced by the windscreen of their cars in the
vertical direction? Assume that hailstones fall vertically and collisions are elastic.

10. A target is located at a point P at a height of 60 m above the ground. A particle is to be projected from a point
O on the ground to hit the target, where OP = 120 m. The minimum possible velocity of projection is
30 x m/s. Find the value of x.

11. A solid sphere of mass 1 kg and radius 10 cm is kept on a horizontal smooth surface. At what height (in cm)
above the centre, a horizontal force of 4 N should be applied so that sphere rolls without slipping ?

12. On a corner on a smooth horizontal surface, we kept 2 masses m1 and m2 attached to a spring as shown.
The spring is initially relaxed and has a spring constant of 150 N/m. Now m2 is suddenly given a velocity to

the left. It is seen that spring first comes to natural length at sec. It next comes to natural length at
5 2

sec. What is mass m1 (in kg)?
10 2

m1 m2

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13. A particle P is travelling along the line ABC as shown in the diagram.

5m
x
A P B C
v

4
The velocity (in ms–1), is given by v = when the particle is x m from A. Given that the particle travels
2x  1

9
from B to C, a distance of 5m, in 12 seconds, and the distance from A to B is   meter. Find the value of n.
n

14. Three blocks A, B, and C, whose masses are 9 kg, 9 kg and 18 kg respectively as shown in the figure, are
released from rest. The coefficient of friction between block A and surface-2 is 0.5 and the coefficient friction
between block B and surface-1 is also 0.5. Find the acceleration (in m/s2) of block C just after release
[Take g =10 m/s2]. All strings and pulleys are ideal. (Round your answer to nearest integer).

Surface-1 B
 = 0.5
A
C
Surface-2  = 0.5

finger finger

15. With two fingers, you hold a cone motionless upside down, as shown
in fig. The mass of the cone is 600 gm, and the coefficient of static
12cm

friction between your fingers and the cone is ( = 0.5). What is the
minimum normal force (in Newton) you must apply with each finger in
order to hold up the cone?

10cm

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 VIBRANT ACADEMY PHYSICS
IRP Class test-3
CLASS TEST - 3
(India) Private Limited JEE ADVANCE
IRP ADVANCE TIME : 75 MIN.
MECHANICS-3
One or more than one correct :
1. Two blocks A and B each of mass ‘m’ are connected by a massless spring of natural length L and spring
constant k. The blocks are initially resting on a smooth horizontal surface. Block C also of mass m moves
on the floor with a speed ‘v’ along the line joining A and B and collides elastically with A then.
(A) The KE of the AB system at max. compression of the spring is zero
(B) The KE of AB system at max compression is (1/4) mv 2

(C) The max compression of spring is v m / k

(D) The maximum compression of spring is v m / 2k

2. A ball collides elastically with a massive wall moving towards it

v 2v
with a velocity v as shown. The collision occurs at a height of h
above ground level and the velocity of the ball just before collision h
is 2v in horizontal direction. Choose the correct option(s).
(A) Velocity of ball after collision 4v w.r.t. ground
(B) Ball moves on parabola after collision
(C) The distance between the foot of the wall and the point on the ground where the ball lands, at the instant

2h
the ball lands, will be 3 v
g

(D) The distance between the foot of the wall and the point on the ground where the ball lands, at the instant

2h
the ball lands, will be 4v
g

3. A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in y
the figure. Choose the correct option(s) C semicircle
r
AB DE
 2r  x
(A) The y-coordinate of the centre of mass of the system is  – 
  2r
semicircle
(B) The Moment of Inertia of the system about x-axis is less than F
its Moment of Inertia about y-axis

9mr 2
(C) The Moment of Inertia of the system about x-axis is where m is the mass of smaller loop BCD
2

11mr 2
(D) The Moment of Inertia of the system about y-axis is where m is the mass of smaller loop BCD
3

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4. A particle is projected so as to graze the tops of two small towers each of height 10 m at a distance of
10 m and 20 m from the point of projection (see figure). Choose the correct option(s).
(A) Horizontal range is 30 m
y
3
(B) tan  =
2
10 m
45
(C) Maximum height from ground is m O 
4 x
10 m 10 m
(D) Time of flight is 3 sec.

5. A solid uniform cylinder of mass M and radius R is pivoted about a fixed horizontal rod at its centre. A
massless inextensible string is wrapped around it, and attached to a block of mass m which is initially at a
height h above the floor. The block is released from rest (see figure). Choose the correct option(s). When
the block hits the floor.
h R
(A) Cylinder has turned by an angle radian
R M
4mgh
(B) Speed of mass m is
2m  M m
(C) Work done by tension on the cylinder is zero h
(D) Work doen by tension on the block is negative

Subjective :
6. Bob of a pendulum of length L is thrown horizontally from its lowest position with an initial speed which is
required to just make the string horizontal. During motion at  = 60° (with the vertical) string snaps. If the
maximum height to which bob rises above the horizontal plane passing through the lowermost point of the
8H
pendulum is H, find the value of .
L

7. A 1 kg block and a rough fixed incline is connected to spring of constant 100 N/m. Block is released from
rest with spring unstretched. The block moves 10 cm down the incline before coming to instantaneous rest.
1
Find the value of .


1k
g
37º


8. A uniform disc is spin with an angular velocity  and simultaneously projected with a linear velocity v
towards left on a plank while the plank moves toward right with a constant velocity 2v. If the disc initially rolls
 nv
without slipping on the plank then angular velocity  = k̂ . The value of n is :
R
y
v

2v x

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9. A disc of mass 'm' is connected to an ideal spring of force constant 'k', on an incline as shown. If disc is
released from rest (when spring is unstretched), what is maximum friction force (in N) on disc during subsequent
motion? Assume that friction is sufficient for pure rolling. Take : mass of disc = 1 kg, Radius of disc = 10 cm,
Angle of incline = 37°.

37º

10. A 200 kg beam 2.0 m in length slides broadside down the ice with a speed of 16 m/s (figure). A 50 kg small
favicol can (guraranteed sticking !!!) at rest sticks at one end as it goes past, both go spinning down the ice.
Assume frictionless motion. What is the angular velocity of combined mass in rad/s.

Horizontal plane

Position of can

11. A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues
to act afterwards. The coefficients of static and sliding friction are 0.5 and 0.4 respectively. What is the
distance (in meter) covered by the body in 4 sec. ?

12. Consider a vertically hanging spring block system. Block of mass m is attached to spring and two blocks of
mass m1 and m2 are placed on it. The system is initially in equilibrium. If block of mass m1 is suddenly lifted
away what should be the value of m2 (in kg), so that the block of mass m2 loses contact with the block of
mass m in the subsequent motion?
(Given : Spring constant k = 1 N/cm, m1 = 5 kg, m = 2 kg)

m2 m1

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13. A flexible rope AB of length L has variable linear density and variable friction coefficient against a surface.
The linear density of rope varies uniformly from  to 2from end A to end B. Friction coefficient varies
uniformly from  to 2 from end A to B. If the external force required to make the rope move on the surface

   gL 
with uniform speed is x   , find the value of x.
 3 

14. A wedge is moving horizontally with constant accn. a = 5 m/s2 rightwards on a horizontal surface. A small
block (initially at rest) travells from the uppermost point to bottom point in 't0' sec. Friction coefficient between
8t 20
block and wedge is  = 0.1. Find the value of (in appropriate SI unit).
5h

'h' a
meter
53º

15. In the following arrangement the system is initially held at rest. The 5 kg block is now released. Assuming the
pulleys and string to be massless and smooth, find the acceleration of block ‘C’ in (cm/s2).

5 kg A

6 kg B C 8 kg

TAKE : g = 9.8 m/s2.

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